/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO

We split firstr-order part and higher-order part, and do modular checking by a general modularity.

******** FO SN check ********
Check non-SN using NTI (Non-Termination Inference by Payet)

******** Computation rules ********
 (1)  fapp(lam(X),Y) => subst(X,Y)
 (2)  subst(v,Y) => Y
 (3)  subst(lam(X),Y) => lam(X)
 (4)  subst(fapp(X,Z),Y) => fapp(subst(X,Y),subst(Z,Y))

backward process killed -- 28 rule(s) generated
forward+backward process killed -- 10 rule(s) generated

NO

let R be the TRS under consideration

subst(fapp(_1,_2),_3) -> fapp(subst(_1,_3),subst(_2,_3)) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0 is a position in r0
we have r0|p0 = subst(_1,_3)
subst(v,_4) -> _4 is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/v, _3/_4} is a mgu of r0|p0 and l'0

==> subst(fapp(v,_1),_2) -> fapp(_2,subst(_1,_2)) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 1 is a position in r1
we have r1|p1 = subst(_1,_2)
subst(v,_3) -> _3 is in R
let l'1 be the left-hand side of this rule
theta1 = {_1/v, _2/_3} is a mgu of r1|p1 and l'1

==> subst(fapp(v,v),_1) -> fapp(_1,_1) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = epsilon is a position in r2
we have r2|p2 = fapp(_1,_1)
fapp(lam(_2),_3) -> subst(_2,_3) is in R
let l'2 be the left-hand side of this rule
theta2 = {_1/lam(_2), _3/lam(_2)} is a mgu of r2|p2 and l'2

==> subst(fapp(v,v),lam(_1)) -> subst(_1,lam(_1)) is in EU_R^3
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {_1/fapp(v,v)}
let theta' = {}
we have r|p = subst(_1,lam(_1)) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = subst(fapp(v,v),lam(fapp(v,v))) is non-terminating w.r.t. R

Termination disproved by the forward process
proof stopped at iteration i=3, depth k=2
9 rule(s) generated
>>NO


******** Signature ********
 fapp : (o,o) -> o
 lam : o -> o
 v : o
 subst : (o,o) -> o
******** Computation Rules ********
 (1)  fapp(lam(X),Y) => subst(X,Y)
 (2)  subst(v,Y) => Y
 (3)  subst(lam(X),Y) => lam(X)
 (4)  subst(fapp(X,Z),Y) => fapp(subst(X,Y),subst(Z,Y))

NO